Taylor series can create harmonics of the frequencies in an input signal. I'm wondering if it is likewise possible to use Volterra series to create sub-harmonics of the frequencies in that signal.
Some degree of finesse is required in posing the question:
Taylor series don't only create harmonics; there's intermodulation distortion as well. Likewise, it's ok with me if a suitable Volterra series doesn't only create sub-harmonics, but also creates something similar to intermodulation distortion, or even some degree of harmonic distortion.
However, I would like to exclude trivial cases where the input signal gets so wrecked that it ends up looking like white noise, which would obviously create sub-harmonics (along with every other frequency you can imagine!). I'm not sure how to formalize this requirement precisely, other than to say that I hope it's clear what I'm driving at.
Here's one way to formalize the behaviour I want:
- Given an input $\cos(\omega t)$, yields an output containing $\cos(\frac{\omega}{n} t)$ for some fixed $n$, ideally a natural number
- Given a general input, a sub-harmonic is generated corresponding to every frequency in the input
- Other "intermodulation distortion"-type artifacts are allowed, "within reason"
The answer can be expressed for either discrete or continuous signals.